Definitions of Supplementary Angles and Linear Pair
Angles _A_ and _B_ are supplementary, as are angles _C_ and _D_.
If $$A+B+C = 280^{\circ}$$, and $$B+C+D = 210^{\circ}$$, what is the value of _A_ + _D_?
Incorrect.
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This is the value of _A_ - _D_. Subtracting the second equation from the first won't give the value of _A_ + _D_ the question asks for.
Incorrect.
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This is the measure of angle _D_, but not the sum of _A_ and _D_.
Incorrect.
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This is equal to _B_ + _C_, but the question asks for _A_ + _D_.
Incorrect.
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Angle _A_ measures 150°, but the question asks for the value of _A_ + _D_.
Very good!
In order to find the value of _A_ + _D_, _A_ and _D_ must first be found individually from the information given in the problem.
First, since _A_ and _B_ are supplementary, and _C_ and _D_ are supplementary,
$$\displaystyle A+B+C+D = (A+B) + (C+D) = 180^{\circ} + 180^{\circ} = 360^{\circ}$$.
Then
$$\displaystyle D = 360^{\circ} - (A+B+C) = 360^{\circ} - 280^{\circ} = 80^{\circ}$$,
and
$$\displaystyle A = 360^{\circ} - (B+C+D) = 360^{\circ} - 210^{\circ} = 150^{\circ}$$.
Therefore, $$A+D = 150^{\circ} + 80^{\circ} = 230^{\circ}$$.
70°
80°
130°
150°
230°
